Let 9 v=9v +g be an infinitesimal deformation of the metric tensor. Demon- strate that the Christoffel symbols Ip and the Riemann tensor Ro change as follows: vp ST" = vp where 1 59 {V89= +V89v -V489,p) , SR = Vvo - V. Additional problem for Daniel, Emmanouil, James and Michael Given a d-dimensional spacetime, consider a Weyl transformation of the metric tensor, 9v = 0 , with o and arbitrary smooth function. (a) Compute the Weyl-transformed Riemann tensor Rgv. (b) Consider the Weyl tensor defined by po = Rp 9pu Pov + go Ppv +9pv Po - gov Ppp, Pv 1 (Rp 2(d - 179R) 1 d = 2 (Ruv d-2 is the so-called Schouten tensor. Demonstrate that Weyl tensor Co is invariant under the Weyl transformation. (c) Demonstrate that the Weyl tensor (i) has all the algebraic properties of the Riemann tensor; and (ii) it is traceless, CP apv=0.